''IF you don't know who Kay Thompson is,'' Rex Reed drawled in a 1972 Harper's Bazaar profile of the writer of the picture book ''Eloise,'' ''please turn the page. You just flunked pizazz.'' Thirty years later, the best-known pizazz machine in the children's-book world is Ian Falconer, the creator of Olivia, a little pig with arty inclinations and a big-as-Lincoln Center personality.

Olivia is a 6-year-old diva-in-training, and she's clearly been minted in the Eloise mold. Unlike Eloise, Olivia doesn't stride through the Plaza Hotel like a pint-size Patton; she lives instead with her family in a tidy Manhattan apartment. But Olivia resembles Eloise in both her fits of pique and her embryonic sense of chic. Olivia pops off the page as if she's just had a ''Queer Eye for the Straight Pig'' makeover -- she's part Babe, part Liza Minnelli, hear her pipsqueak roar. Among her favorite things: high heels, Degas, accessories, Maria Callas.

Falconer's first Olivia book, titled simply ''Olivia,'' appeared in 2000 and became, in that oxymoronic phrase, an instant classic. If you happened to have children who were between 2 and 7 in 2000, you knew ''Olivia'' was going to be a big deal because, at birthday parties and on Christmas morning, people kept giving your children copies of it. Or rather, people kept giving you copies of it, because ''Olivia'' is one of those kids' books, filled as it is with references to Callas and Jackson Pollock and the ballet, that hip mommies and daddies like to give to the children of other hip mommies and daddies in order to demonstrate, yet again, what delightfully hip mommies and daddies we all are. (Bonus: ''Olivia'' looks great on a coffee table.)

While the parents were busily flattering their own good taste, the children, in my experience, thought ''Olivia'' was just sort of O.K. My kids politely tolerate Falconer's book, but it's not one they run to at bedtime and squeeze to their chests. My children aren't dormice, but I suspect that on some level they feel about the brassy Olivia the way I once felt about the entitled Eloise: ''Boy, is she going to grow up to be a monster.'' People with pizazz have always made me want to crawl under a table.

Having said all that, I can't deny that the Olivia books -- there are now three of them -- coast a long way on the substantial charm that Falconer pours into them. An artist who has done more than a dozen New Yorker covers as well as designing sets for the stage, Falconer has a witty and sophisticated eye; there are images in each of his books that can make you laugh with instant recognition. (In ''Olivia,'' the drawing of little Olivia trying to carry the family's cat, which is almost as big as she is, is -- as anyone who's had kids and cats can tell you -- a sliver of comic genius.)

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The crisp look of Falconer's books also sets them apart. In the first Olivia book, the color scheme was almost entirely black, grays and a bright lipstick red against a white background. In ''Olivia Saves the Circus,'' Falconer's second book, he added pink to his palette. Now, in ''Olivia . . . and the Missing Toy,'' there's a smattering of green as well. These books look timeless, and they feel that way, too -- there are only a few clues (in the first book, Olivia gets a ''time out'') that we're in contemporary New York as opposed to the New York of the 1940's or 50's. A reference to ''Blue's Clues'' or ''SpongeBob SquarePants'' or rap music would shatter the mood here. If anyone in Olivia's family owned an iPod, all it would dispense would be Bobby Short tunes.

The title of Falconer's new book tells you a good deal about the subject matter he's dealing with here -- and this book arrives at a moment when there is a flurry of just-published volumes about lost toys, including John Stadler's ''Catilda'' and Neil Gaiman and Dave McKean's best-selling (and quite dark) ''Wolves in the Walls.'' This is a venerable genre, of course, even if one of its greats, Jules Feiffer's magnificent ''I Lost My Bear,'' is only five years old. It's reasonable, given the topsy-turvy state of the world over the past two years, that the real and potential loss of comforting realities might be on children's minds as much as it is on adults'. These are books to acknowledge and calm cases of the jitters.

''Olivia . . . and the Missing Toy'' begins, before the title page, with a terrific series of drawings, 12 of them spread across two pages, of Olivia trying to prop up, and then serve tea to, a favorite old battered one-eyed doll. Before long, however, we see Olivia dreaming of riding a camel in Egypt -- the importance of having Big Dreams is the primal theme of the Olivia books -- and then being waked for a soccer game. She's annoyed at the color of her team shirt (''Olivia's uniform comes in a really unattractive green''), and she asks her mom to make her a red shirt instead. ''But then you'll look different from everyone else on the team,'' her mother says. Olivia, being Olivia, replies, ''That's the point.''

IN the last Olivia book, there was, for no discernible reason, a large black-and-white photograph of Eleanor Roosevelt hanging over Olivia's bed. This time there's an outsize photograph of Martha Graham on the wall; she's in middance and pressing her wrist to her head as if she has a 10-ton migraine. Falconer doesn't comment on these images; they have been put there, one supposes, by Olivia's parents, to provide their daughter with some free-thinking female role models. I know parents who are glad to be given, by Ian Falconer, the opportunity to explain to their children who Roosevelt and Graham were. I know other parents -- I'm one of them -- for whom these photographs cause the needle on the Acme Pretentiousness Meter to spin violently off its axis and fly into low-level orbit around the earth.

The story of the missing toy plays out pretty quickly. As Olivia's mother finishes sewing a red soccer shirt for her, Olivia suddenly notices that her battered favorite doll has gone missing. The tantrum she throws is both funny and believable, and the drawings of Olivia searching for the doll -- she lifts up an improbably large sofa, and then the cat -- are sly and charming. The toy is found, of course, after a small amount of mildly spooky ''Phantom of the Opera''-type theatrics on ''a dark and stormy night.'' Olivia's doll is returned in even worse shape than it was in before. But Olivia fixes it up as best she can, and she forgives the perpetrator. It's a sweet ending to a mild and modest book, one that proves yet again that, as Charlotte the spider once spun it about Wilbur, Olivia is Some Pig.